Our work is mainly related to the study of proportional representation in committee elections, and in particular approval-based committee elections, which are surveyed in [1]}. In recent years, there has been increased interest in studying online versions of voting problems. Proportionality is studied in [2]} who formalize voting streams, a setting in which alternatives are fixed, but voters arrive in an online manner, which is the opposite to ours. In [3]}, the sets of voters and alternatives are fixed, but the valuations of each voter for an alternative varies over time. Utilities are defined at each timestep as the cumulative reward of each agent given past decisions, and the goal is to maximize Nash social welfare. [4]} consider a similar setting with ordinal preferences instead of cardinal valuations, and study voting rules that weight agents according to their past satisfaction. [5]} address the partial observability of voters' preferences.
